Use the given data set to complete parts(a) through(c) below.(Use =0.05.)

x

10

8

13

9

11

14

6

4

12

7

5

y

9.15

8.14

8.73

8.77

9.25

8.09

6.14

3.11

9.14

7.26

a. Construct a scatterplot. Choose the correct graph below.

A.

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 6); (5, 5.6); (6, 5); (7, 4.6); (8, 4); (9, 3.6); (10, 3); (11, 2.6); (12, 2); (13, 1.6); (14, 1).

B.

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 3.2); (5, 4.8); (6, 6.2); (7, 7.2); (8, 8.2); (9, 8.8); (10, 9.2); (11, 9.2); (12, 9.2); (13, 8.8); (14, 8).

C.

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 1); (5, 1.4); (6, 1.6); (7, 2); (8, 2.4); (9, 3); (10, 3.6); (11, 4.2); (12, 4.8); (13, 6); (14, 8).

D.

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 2); (5, 2.6); (6, 3); (7, 3.6); (8, 4); (9, 4.6); (10, 5); (11, 5.6); (12, 6); (13, 6.6); (14, 7).

b. Find the linear correlationcoefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

The linear correlation coefficient is r=__

Using the linear correlation coefficient found in the previousstep, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below.

A.

There is insufficient evidence to support the claim of a nonlinear correlation between the two variables.

B.

There is insufficient evidence to support the claim of a linear correlation between the two variables.

C.

There is sufficient evidence to support the claim of a nonlinear correlation between the two variables.

D.

There is sufficient evidence to support the claim of a linear correlation between the two variables.

c. Identify the feature of the data that would be missed if part(b) was completed without constructing the scatterplot. Choose the correct answer below.

A.

The scatterplot reveals a distinct pattern that is astraight-line pattern with negative slope.

B.

The scatterplot does not reveal a distinct pattern.

C.

The scatterplot reveals a distinct pattern that is astraight-line pattern with positive slope.

D.

The scatterplot reveals a distinct pattern that is not astraight-line pattern.

Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs ofpeople, the linear correlation coefficient is 0.927 and the equation of the regression line is y=11.25+1.12x, where x represents the IQ score of the twin born second. Also, the 20 x values have a mean of 93.1 and the 20 y values have a mean of 92.7. What is the best predicted IQ of the twin born first given that the twin born second has an IQ of 95? Use a significance level of 0.05.

The best predicted IQ of the twin born first is

a. Using the pairs of values for all 10 points, find the equation of the regression line.

b. After removing the point with coordinates (1,2), use the pairs of values for the remaining 9 points and find the equation of the regression line.

c. Compare the results from parts(a) and(b).

A scatterplot has a horizontal x-scale from 0 to 10 in increments of 1 and vertical y-scale from 0 to 10 in increments of 1. Ten points are plotted with nine points, (3, 5), (4, 5), (5, 5), (3, 6), (4, 6), (4, 6), (5, 6), (3, 7), (4, 7), and (5, 7), forming a square and the tenth point (1, 2) being below and to the left of the square.

a. What is the equation of the regression line for all 10 points?

y=__+__x

b. What is the equation of the regression line for the set of 9 points?

y =__

c. Choose the correct description of the results below.

A.

The regression line is very similar in both cases.

B.

The regression linechanges, but the change is small.

C.

The removal of the point has a significant impact on the regression line.

D.

There is no regression line for the second case because the data are in a pattern.